value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Word problem, A girl has 25 plants in all, 8 of them are tomatos. She has 1...

A girl has 25 plants in all, 8 of them are tomatos. She has 10 more bean plants than pepper plants. How many pepper plants does she have?

Prove that 2b3-3abc+a2d=0, If  the  ratios  of  the  polynomial ax 3 +3bx...

If  the  ratios  of  the  polynomial ax 3 +3bx 2 +3cx+d  are  in  AP,  Prove  that  2b 3 -3abc+a 2 d=0 Ans: Let p(x) = ax 3 + 3bx 2 + 3cx + d and α , β , r are their three Z

Polynomials, zeroes of polynomial 2x2-3x-2

zeroes of polynomial 2x2-3x-2

..Job, Eddie mkes $15.75 per hour. Estimate how much Eddie will make per ye...

Eddie mkes $15.75 per hour. Estimate how much Eddie will make per year if he works 40 hours per week and 50 weeks per year.

The definite integral- area under a curve, The Definite Integ...

The Definite Integral Area under a Curve If there exists an irregularly shaped curve, y = f(x) then there is no formula to find out

Erp for a company, recomendation to a company to implement ERP to succeed

recomendation to a company to implement ERP to succeed

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd